@whuber added edit, hope this clarifies. The property being estimated is the total sum divided by len(bucket), and it is necessary to include customers who did not purchase anything during the experimentation period because the treatment is expected to work by enticing customers to make a purchase (imagine amazon etc. where people have accounts and sometimes make purchases). Finally the information I have on the rest of the population is: I know both control and treatment has the same population size, though I don't know how big.

Thanks for your answer. Suppose however that my features are embeddings that have good linear substructures (like GloVe vectors). Shouldn't I then expect to find translation invariant features across the hyperspace? Say presence of both of the words "King" and "Man" is informative. I'd imagine a convnet would be able to generalize that to "Queen" and "Woman" - would a feed-forward network also be able to exploit that sort of thing?